The following information is given for proportioning a cantilever footing with reference to Fig. 14.2.
Column Loads: Q_{1}=1455 kN , Q_{2}=1500 kN.
Size of column: 0.5 x 0.5 m.
L_{c}=6.2 m , q_{s}=384 kN / m ^{2}It is required to determine the size of the footings for columns 1 and 2.
Assume the width of the footing for column 1=B_{1}=2 m.
First trial
\text { Try } e=0.5 m \text {. Now, } L_{R}=6.2-0.5=5.7 m.
Reactions
R_{1}=Q_{1} 1+\frac{e}{L_{R}}=14551+\frac{0.5}{5.7}=1583
R_{2}=Q_{2}-\frac{Q_{1} e}{L_{R}}=1500-\frac{1455 \times 0.5}{5.7}=1372 kN
Size of footings – First trial
Col. 1. Area of footing A_{1}=\frac{1583}{384}=4.122 sq . m
Col. 2. Area of footing A_{2}=\frac{1372}{384}=3.57 sq \cdot m
Try 1.9 x 1.9m
Second trial
New value of e=\frac{B_{1}}{2}-\frac{b_{1}}{2}=\frac{2}{2}-\frac{0.5}{2}=0.75 m
New L_{R}=6.20-0.75=5.45 m
R_{1}=14551+\frac{0.75}{5.45}=1655 kN
R_{2}=1500-\frac{1455 \times 0.75}{5.45}=1300 kN
A_{1}=\frac{1655}{384}=4.31 sq \cdot m \text { or } 2.08 \times 2.08 m
A_{2}=\frac{1300}{384}=3.38 sq \cdot m \text { or } 1.84 \times 1.84 m
Check e=\frac{B_{1}}{2}-\frac{b_{1}}{2}=1.04-0.25=0.79 \approx 0.75 m
Use 2.08 x 2.08 m for Col. 1 and 1.90 x 1.90 m for Col. 2.
Note: Rectangular footings may be used for both the columns.